SOLUTION: completing the square -1/2x²+4x-6=0

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Question 108379: completing the square
-1/2x²+4x-6=0
Found 2 solutions by stanbon, Fombitz:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
-1/2x²+4x-6=0
Multiply thru by -2 to get:
x^2-8x+12 = 0
Complete the square on the x terms and keep the equation balanced.
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x^2-8x = -12
x^2-8x+16 = -12+16
(x-4)^2 = 4
--------------
Take the square root of both sides to get:
x-4 = 2 or x-4 = -2
x = 6 or x = 2
====================
Cheers,
Stan H.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
-%281%2F2%29x%5E2%2B4x-6=0
Let's multiply both sides by (-2) to get rid of the fraction.
%28-2%29%28-%281%2F2%29x%5E2%2B4x-6%29=0
x%5E2-8x%2B12=0Simplify.
We want to find a constant, a, such that,
%28x%2Ba%29%5E2=x%5E2%2B2ax%2Ba%5E2Expand the perfect square equation.
Compare coefficients of that equation with your equation,
2ax=-8x
a=-4
If a=-4, the a%5E2=16.
In order get get 16 on the left hand side of the equation, that is, in order to complete the square, you need to add 4 to the left hand side.
Whatever you do to one side of the equation, you must do to the other side.
x%5E2-8x%2B12=0
x%5E2-8x%2B16=4Add 4 to both sides.
%28x-4%29%5E2=4Complete the square.
x-4=2 and x-4=-2
x-4=2
highlight%28x=6%29
x-4=-2
highlight%28x=2%29
Check your answers.
-%281%2F2%29x%5E2%2B4x-6=0
-%281%2F2%29%286%29%5E2%2B4%286%29-6=0
-18%2B24-6=0
0=0
-%281%2F2%29x%5E2%2B4x-6=0
-%281%2F2%29%282%29%5E2%2B4%282%29-6=0
-2%2B8-6=0
0=0
Both answers lead to true statements.
Good answers.